James H. Nolen

  • Associate Professor of Mathematics
External address: 243 Physics Bldg, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2862
Office Hours: 

Mondays, 1-2:30
Wednesdays, 10:30-12

Research Areas and Keywords

Analysis
partial differential equations, probability, asymptotic analysis, homogenization
Biological Modeling
asymptotic analysis
PDE & Dynamical Systems
reactive diffusion equations & applications, homogenization of partial differential equations, random media, asymptotic analysis
Physical Modeling
asymptotic analysis
Probability
homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

I study partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. In many cases, the parameters for such equations are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in equations modeling random phenomena and whether one can describe the statistical properties of the solution to these equations. For example, I have worked on nonlinear partial differential equations that describe waves and moving interfaces in random media. This work involves ideas from both analysis and probability.   I also study the asymptotic behavior of stochastic processes.

Education & Training
  • Ph.D., University of Texas at Austin 2006

  • B.S., Davidson College 2000

Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields 159.3-4 (2014): 661-700. Full Text

Nolen, J. "Normal approximation for a random elliptic equation." Probability Theory and Related Fields (2013): 1-40. Full Text

Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 2238-2258. (Academic Article) Full Text Open Access Copy

Mellet, A, and Nolen, J. "Capillary drops on a rough surface." Interfaces and Free Boundaries 14.2 (2012): 167-184. Full Text

Nolen, J, Roquejoffre, J-M, Ryzhik, L, and Zlatoš, A. "Existence and Non-Existence of Fisher-KPP Transition Fronts." Archive for Rational Mechanics and Analysis 203.1 (2012): 217-246. Full Text

Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted)." Networks and Heterogeneous Media (2012). (Academic Article)

Matic, I, and Nolen, J. "A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation." Journal of Statistical Physics 149.2 (2012): 342-361. Full Text

Nolen, J. "A central limit theorem for pulled fronts in a random medium." Networks and Heterogeneous Media 6.2 (2011): 167-194. Full Text

Cardaliaguet, P, Nolen, J, and Souganidis, PE. "Homogenization and Enhancement for the G-Equation." Archive for Rational Mechanics and Analysis 199.2 (2011): 527-561. Full Text

Nolen, J, and Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." Communications in Mathematical Sciences 9.2 (2011): 561-582.

Pages